document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013006>Question 1013006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what values of k will the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > have roots that are equal but opposite in sign </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629163 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "to have roots that are equal but opposite in sign, we can write our equation like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-x%29%5E2+-%28k-2%29%28-x%29-12=0 ALIGN=MIDDLE  ALT=\"+%28-x%29%5E2+-%28k-2%29%28-x%29-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And since we started with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we can set the left sides equal:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=++%28-x%29%5E2+-%28k-2%29%28-x%29-12+ ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=++%28-x%29%5E2+-%28k-2%29%28-x%29-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-kx%2B2x-12=+x%5E2+%2Bkx-2x-12+ ALIGN=MIDDLE  ALT=\"+x%5E2+-kx%2B2x-12=+x%5E2+%2Bkx-2x-12+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cross%28x%5E2+%29-k%2Across%28x%29%2B2cross%28x%29-cross%2812%29=+cross%28x%5E2%29+%2Bkx-2cross%28x%29-cross%2812%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-k%2B2=+k-2+ ALIGN=MIDDLE  ALT=\"+-k%2B2=+k-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2B2=+k%2Bk+ ALIGN=MIDDLE  ALT=\"+2%2B2=+k%2Bk+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4=+2k+ ALIGN=MIDDLE  ALT=\"+4=+2k+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2 ALIGN=MIDDLE  ALT=\"k=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%28k-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%28k-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%282-2%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%282-2%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-%280%29x-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2+-%280%29x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2-12=0 ALIGN=MIDDLE  ALT=\"+x%5E2-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2=12 ALIGN=MIDDLE  ALT=\"+x%5E2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=sqrt%2812%29 ALIGN=MIDDLE  ALT=\"+x=sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=sqrt%284%2A3%29 ALIGN=MIDDLE  ALT=\"+x=sqrt%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"+x=2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"+x=2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"+x=-2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );